Success comes with consequences, and one of them is contempt. As the South by Southwest music festival's attendance has risen — from just 700 in 1987 to nearly 30,000 in 2015 — so too has the volume of the critics and contrarians who've gone on to vilify what's become the world's largest music event.

On the cover of her new 14th set, Unrepentant Geraldines, adventurous singer-songwriter-keyboardist Tori Amos is standing before a wall-size mural, a paintbrush clutched in her right hand, as if she's just put the finishing strokes on her latest primary-colored masterpiece. But don't read it too literally, she cautions...